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Center of a Circle Calculator

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Welcome to the center of a circle calculator that finds the center of a circle for you. Here, we'll show you how to calculate the center of a circle from the various circle equations. We'll also cover finding the center of a circle without any math!

How do I use the center of a circle calculator?

The center of a circle calculator is easy to use.

  1. Select the circle equation for which you have the values.
  2. Fill in the known values of the selected equation.
  3. You can find the center of the circle at the bottom.

Read on if you want to learn some formulas for the center of a circle!

How do I calculate the center of a circle?

Circles can be defined with multiple equations. If you have a mathematical formula for your circle, pick the correct one from the headings below. We'll then explain how to calculate the center of the circle from there.

The standard equation of a circle

The standard equation of a circle is:

(x−A)2+(y−B)2=C\small (x - A)^2 + (y - B)^2 = C

where C=r2C = r^2, or the radius squared.

With this equation, we can find the center of the circle at point (A,B)(A, B). Be careful of the signs!

The parametric equation of a circle

The parametric equation of a circle is defined as:

x=A+r ⁣⋅ ⁣cos⁡(α)y=B+r ⁣⋅ ⁣sin⁡(α)\small \begin{split} x &= A + r\!\cdot\!\cos{(\alpha)} \\ y &= B + r\!\cdot\!\sin{(\alpha)} \end{split}

In this form, we can calculate the center of the circle as (A,B)(A,B) again.

The general equation of a circle

A less common circle equation is the general equation of a circle:

x2+y2+D ⁣⋅ ⁣x+E ⁣⋅ ⁣y+F=0\small x^2 + y^2 + D\!\cdot\!x + E\!\cdot\!y + F = 0

In the general equation, we can calculate the center of the circle as (−D2,−E2)\left(-\frac{D}{2}, -\frac{E}{2}\right).

How do I find the center of a physical circle?

If you have a circle drawn on paper, there's no center of a circle formula. Instead, follow these steps:

  1. Draw two (or more) chords on the circle.
  2. Find these chords' midpoints.
  3. From the midpoints, draw lines that are perpendicular to the chords.
  4. The point where these lines intersect is the circle's center.
  5. Congrats, you can find the center of the circle!
FAQs

What is the center of a circle represented by the equation (x+9)² + (y−6)² = 10²?

The center of this circle is (−9, 6), with a radius of 10. The equation (x+9)² + (y−6)² = 10² is in the standard circle equation form (x−A)² + (y−B)² = C, making A = −9 and B = 6.

What is the center of a circle represented by the equation (x−5)² + (y+6)² = 4²?

The center of this circle is (5, −6), with a radius of 4. The equation (x−5)² + (y+6)² = 4² is in the standard circle equation form (x−A)² + (y−B)² = C, making A = 5 and B = −6.

What is the center of a circle given the equation (x−5)² + (y+7)² = 81?

The center of this circle is (5, −7), with a radius of √81 = 9. The equation (x−5)² + (y+7)² = 81 is in the standard circle equation form (x−A)² + (y−B)² = C, making A = 5 and B = −7.

Standard

(x − A)² + (y − B)² = C

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